Enter the raw data point, population mean, and standard deviation into the calculator below to determine the z-score, also known as the standard score.

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## Z-Score Formula

The following formula is used to calculate the z-score:

- Where
*μ*is the mean of the population - and
*σ*is the standard deviation of the population - x is the raw data point

The Z score can also be determined using a table such as provided below.

## Z Score Definition

A z-score, also known as a standard score, is a term used in statistics to describe a signed fractional number of standard deviations by which the value of a data point is above the mean value.

A Z-score is used to compare observational data to theoretical deviation. Determining the z-score requires that one knows the mean and standard deviation of a total population that the data in question belongs to.

Since z-score is used to compare observed data to theoretical data, another way of looking at it is to say that it’s a measure of confidence in a data set. This means that a z-score directly correlates with a confidence interval

## How to calculate a z-score?

The following is a step by step guide on how to calculate the z-score:

- Through analyzing the formula above, we know the first step will be to acquire the mean of the population.
- For this example, we will assume the mean is 20.
- The next step is to determine the standard deviation of the population. For this example let’s assume the deviation is 1.5.
- Finally, we must measure our raw data value of x. We find that x is 25.
- The last step is to plug all of this information into the formula above to get our answer. We find the z-score of this problem to be 3.33

Analyze your results and apply to future problems.

## FAQ

**What does a Z-Score indicate?**

A Z-Score indicates how many standard deviations an element is from the mean. A positive Z-Score means the data point is above the mean, while a negative Z-Score means it’s below the mean.

**Why is the Z-Score important in statistics?**

The Z-Score is important because it allows for comparisons between different data sets or within the same data set over time, and it helps identify outliers.

**Can Z-Scores be used for all types of data?**

Z-Scores are most effective with data that is normally distributed. For data that does not follow a normal distribution, other methods of standardization might be more appropriate.

**How does the Z-Score relate to the standard normal distribution?**

The Z-Score is a key part of the standard normal distribution. It is used to determine where a data point lies within the distribution, helping to calculate probabilities and confidence intervals.